scholarly journals Existence of positive solutions for the nonlinear elastic beam equation via a mixed monotone operator

2018 ◽  
Vol 327 ◽  
pp. 306-313 ◽  
Author(s):  
I.J. Cabrera ◽  
B. López ◽  
K. Sadarangani
Keyword(s):  
Positive Solutions ◽  
Monotone Operator ◽  
Elastic Beam ◽  
Beam Equation ◽  
Mixed Monotone Operator ◽  
Elastic Beam Equation ◽  
Existence Of Positive Solutions ◽  
Nonlinear Elastic

scholarly journals Positive solutions for nonlinear elastic beam models

2001 ◽  
Vol 27 (6) ◽  
pp. 365-375 ◽  
Author(s):  
Bendong Lou
Keyword(s):  
Positive Solutions ◽  
Elastic Beam ◽  
Negative Answer ◽  
Existence Of Positive Solutions ◽  
Nonlinear Elastic ◽  
Positive Results

We give a negative answer to a conjecture of Korman on nonlinear elastic beam models. Moreover, by modifying the main conditions in the conjecture (generalizing the original ones at some points), we get positive results, that is, we obtain the existence of positive solutions for the models.

scholarly journals Existence of Positive Solutions of a Discrete Elastic Beam Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Ruyun Ma ◽  
Jiemei Li ◽  
Chenghua Gao
Keyword(s):  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Boundary ◽  
Global Bifurcation ◽  
Elastic Beam ◽  
Beam Equation ◽  
Nonlinear Boundary Value Problems ◽  
Order Difference ◽  
Bifurcation Theorem ◽  
Existence Of Positive Solutions

LetTbe an integer withT≥5and letT2={2,3,…,T}. We consider the existence of positive solutions of the nonlinear boundary value problems of fourth-order difference equationsΔ4u(t−2)−ra(t)f(u(t))=0,t∈T2,u(1)=u(T+1)=Δ2u(0)=Δ2u(T)=0, whereris a constant,a:T2→(0,∞),  and  f:[0,∞)→[0,∞)is continuous. Our approaches are based on the Krein-Rutman theorem and the global bifurcation theorem.

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